Challenge #1: Sketch the DERIVATIVE of the graph shown here. -4. -8 -4 4 8 -4

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Sketch the derivative of the graph shown here

 

**Challenge #1: Sketch the DERIVATIVE of the graph shown here.**

The image depicts a graph with a red line on a coordinate plane. This line passes through the origin (0,0) and has a positive slope. Specifically, the line appears to follow the equation \( y = x \), as it rises one unit for every unit it moves to the right.

**Explanation of Graph:**

- **Axes:** The graph has standard x and y axes, with the origin at coordinate (0,0). Both axes are marked at intervals of 2, ranging from -8 to 8 on the x-axis and -4 to 4 on the y-axis.
- **Line:** The red line in the graph has a uniformly positive slope, indicating a constant rate of change.
- **Derivative:** The slope of the line is constant, suggesting that its derivative is also constant. Since this line appears to be \( y = x \), the derivative \( y' \) is 1.

Therefore, the derivative of this graph is a horizontal line at \( y = 1 \) across the graph.
Transcribed Image Text:**Challenge #1: Sketch the DERIVATIVE of the graph shown here.** The image depicts a graph with a red line on a coordinate plane. This line passes through the origin (0,0) and has a positive slope. Specifically, the line appears to follow the equation \( y = x \), as it rises one unit for every unit it moves to the right. **Explanation of Graph:** - **Axes:** The graph has standard x and y axes, with the origin at coordinate (0,0). Both axes are marked at intervals of 2, ranging from -8 to 8 on the x-axis and -4 to 4 on the y-axis. - **Line:** The red line in the graph has a uniformly positive slope, indicating a constant rate of change. - **Derivative:** The slope of the line is constant, suggesting that its derivative is also constant. Since this line appears to be \( y = x \), the derivative \( y' \) is 1. Therefore, the derivative of this graph is a horizontal line at \( y = 1 \) across the graph.
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